Related papers: A Scalable Algorithm for Two-Stage Adaptive Linear…
Two-stage stochastic programs (2SPs) are important tools for making decisions under uncertainty. Decision-makers use contextual information to generate a set of scenarios to represent the true conditional distribution. However, the number…
Column generation is a widely used decomposition technique for large-scale linear programs, but it often suffers from slow convergence due to poor initial dual estimates and dual oscillations. Stabilization techniques such as smoothing and…
Column generation is often used to solve multi-commodity flow problems. A program for column generation always includes a module that solves a linear equation. In this paper, we address three major issues in solving linear problem during…
Attack Graph (AG) represents the best-suited solution to support cyber risk assessment for multi-step attacks on computer networks, although their generation suffers from poor scalability due to their combinatorial complexity. Current…
Graph data structures are fundamental for studying connected entities. With an increase in the number of applications where data is represented as graphs, the problem of graph generation has recently become a hot topic. However, despite its…
The unit commitment problem is an important optimization problem in the energy industry used to compute the most economical operating schedules of power plants. Typically, this problem has to be solved repeatedly with different data but…
This paper considers the learning of Boolean rules in disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) as an interpretable model for classification. An integer program is formulated to optimally trade…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
In recent years, significant progress has been made in the development of text-to-image generation models. However, these models still face limitations when it comes to achieving full controllability during the generation process. Often,…
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…
Sparse ridge regression is widely utilized in modern data analysis and machine learning. However, computing globally optimal solutions for sparse ridge regression is challenging, particularly when samples are arbitrarily given or generated…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
Set covering problem is an important class of combinatorial optimization problems, which has been widely applied and studied in many fields. In this paper, we propose an improved column generation algorithm with neural prediction (CG-P) for…
As a common method in Machine Learning, Ensemble Method is used to train multiple models from a data set and obtain better results through certain combination strategies. Stacking method, as representatives of Ensemble Learning methods, is…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
We propose a unified approach for bottom-up hierarchical image segmentation and object proposal generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm.…
This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…
It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use…
Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…